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Vertical localization issues in LETKF

Breogan Gomez, Andreas Rhodin, Hendrik Reich

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Perform single observation experiments and study the vertical impact. In situ observations and radiances.

First attempt to understand the behavior of the LETKF.

Explore the fundamental limitations of EnKF or LETKF algorithms (i.e. un-localized obs. such as radiance obs.)

Objectives

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LETKF – Localized Ensemble Transform Kalman Filter

Horizontal

VerticalIntegral gives one number, but where to apply it!

Vloc

Similar to a Gaussian but function equals 0 at aprox. 3 times Vloc

Localization function

Analysis are independent for every grid point

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Background Ensemble

B-matrix 128 random perturbations

3DVAR first guess

128 ensemble members. (Same error covariance

statistics as 3DVAR)+

3DVAR and LETKF should give equal results for a large (infinity) number member of ensemble members. This means that, for comparison purposes, 3dvar can be regarded as the reference to match.

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Objective is to study the impact of a surface pressure observation on a vertical profile.

A single surface observation from a rawinsonde is chosen at a random location.

Single sfc pressure observation

LETKF and 3DVAR allows to select the prognostic variable to analyze. (geopot. height or temperature).

Finally different vertical localization values are chosen to see the different impacts: 1.00, 0.60, 0.30, 0.15 (Those are eq. to the sigma of a gaussian distribution in log(P)).

Parameters to study

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Assimilated in Geopot. height

Assimilated in Temperature

Geopot. height increments Temperature increments

Assimilation in Geop. height or Temperature values Single sfc pressure Obs

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Objective is to study the impact of a radiance observation on a vertical profile.

A single random location is chosen and only some channels are studied. AMSUA: 5, 7 and AMSUB: 3, 4, 5.

Different vertical localization values: 10.0, 1.2, 0.6, 0.3. Only geopotential height values are used this time.

Radiance observations

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Nominal height values for radiances

AMSUA7 Sensitivity functions for temperature and relative humidity

AMSUB4 Sensitivity functions for temperature and relative humidity

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Standard Deviation

AMSUA5 - Temperature Increments match 3dvar between 0.6 and 1.2

AMSUB4 - RH Increments already have a good agreement with 3dvar between 0.3 and 0.6

AMSUA5 AMSUA7 AMSUB3 AMSUB4 AMSUB5

StdDev 0.65 0.82 0.45 0.34 0.33

StdDev is higher for AMSUA than AMSUB(Values in LogP comparable to Vloc)

rhbirhtbit HH

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In situ and radiance observations

Geopotential height /

Temperature

Relative humidity

Tropics 0.38 0.13

Extratropics 0.93 0.20

Vertical correlation length scale in LogP

AMSUA AMSUB5

StdDev 0.60-0.80 0.30-0.40

Standard deviation in LogP

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In situ and radiance observations

Objective is to study the impact of a radiance observation on a vertical profile.

We want to threat this observations with different vlocs values as they are of a different physical kind.

Different vertical localization values (10.0, 1.2, 0.6, 0.3, 0.15) are used for an in-situ obs. meanwhile a radiance observation has a fixed value of 1.2. (Fertig et al. 2007)

AMSUA5 and an artificial rawinsonde measurement at 800HPa were used. (We impose a obs. minus first guess equal to the standard error of each observation.)

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Temperature increments

AMSUA5

AMSUA5 +

Temp 800HPa

Temp 800HPa

The over-shooting is reduced, while still matching the in-situ observation.

But still we can have some balance problems when Vloc is small for in-situ observations.

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Some problems found

AMSUB3

Noisy increments.

Many member are close to zero!AMSUB5

Relative Humidity Increments

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One should consider which diagnostic variables are used in the analysis. (In this case geopotential height or temperature, may be others)

A method to estimate the nominal height of radiance observations has been proposed. Satisfactory results so far.

Summary and Conclusions

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Summary and Conclusions

Localization of non local observations (radiances)

Non linearity (relative humidity increments)

Localization of variables of very different length scales.

Single location experiments: need to do global experiments with a full set of observation and perform some statitistics (e. g. RMSE)

Aspects not handled satisfactorily yet.

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Thank you

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Apendix - Nominal height for radiance obs.

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